Please help on this thermodynamics problem! The entropy vs energy for two system

Question

Please help on this thermodynamics problem! The entropy vs energy for two systems is shown in the graph below. Each system is plotted separately on the same graph with the same scale(i.e. this is not the total entropy, just the entropy vs energy for each system, and on the energy axis, both U_A and U_B increase when going to the right). The systems start each with 10 units of energy. What will happen to the energy of each system when the systems are placed in thermal contact? Estimate the final energy of each system after they reach equilibrium. (Be sure to explain your reasoning!)

Explanation / Answer

Since the systems had initially same energy and the energy added is also same only thing different is the entropy that might be becuase of difference in the number of particles or size of particles. Because of same energy at the point of just being before in a thermal contact and still being isolated, assuming no mixing of system A and B takes place, therefore we can say that enrgy is going to be Ufinal = Uinitial + 20 = 30 for both systems

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